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LEADER 03294cam 2200433Ii 4500

001 ocn878024329;

003 OCoLC;

005 20150428112930.0;

008 140423t20142014maua b 001 0 eng d;

020 a| 1571462880;

020 a| 9781571462886;

035 a| (Sirsi) 99961939379;

035 a| 99961939379;

035 a| (OCoLC)878024329;

050 4 a| QA374b| .L529 2014;

082 04 a| 515.7232| 23;

084 a| 37-02a| 37K35a| 37K40a| 35Q51a| 35Q412| msc;

100 1 a| Li, Charles,d| 1965-=| ^A1247828;

245 10 a| Lie-bäcklund-darboux transformations /c| Y. Charles Li, Artyom Yurov.;

264 1 a| [Somerville, Mass. ; a| Beijing, China] :b| International Press and Higher Education Press,c| [2014];

300 a| ix, 160 pages :b| illustrations ;c| 26 cm.;

336 a| textb| txt2| rdacontent;

337 a| unmediatedb| n2| rdamedia;

338 a| volumeb| nc2| rdacarrier;

490 1 a| Surveys of modern mathematics ;v| v. 8;

504 a| Includes bibliographical references (p. [155]-160) and index.;

505 0 a| 1. Introduction -- 2. A brief account on Bäcklund transformations -- 3. Nonlinear Schrödinger equation -- 4. Sine-Gordon equation -- 5. Heisenberg ferromagnet equation -- 6. Vector nonlinear Schrödinger equations -- 7. Derivative nonlinear Schrödinger equations -- 8. Discrete nonlinear Schrödinger equation -- 9. Davey-Stewartson II equation -- 10. Acoustic spectral problem -- 11. SUSY and spectrum reconstructions -- 12. Darboux transformations for Dirac equation -- 13. Moutard transformations for the 2D and 3D Schrödinger equations --14. BLP equation -- 15. Goursat equation -- 16. Links among integrable systems.;

520 3 a| This is an interdisciplinary monograph at the cutting edges of infinite dimensional dynamical systems, partial differential equations, and mathematical physics. It discusses Y. Charles Li's work of connecting Darboux transformations to homoclinic orbits and Melnikov integrals for integrable partial differential equations; and Artyom Yurov's work in applying Darboux transformations to numerous areas of physics. Of particular interest to the reader might be the brand-new methods, developed by Li in collaboration with others, of using Darboux transformations to construct homoclinic orbits, Melnikov integrals, and Melnikov vectors for integrable systems. It should be noted that integrable systems (also named soliton equations) are the infinite dimensional counterparts of finite dimensional integrable Hamiltonian systems. What the new methods reveal are the infinite dimensional phase space structures. This work is intended for advanced undergraduates, graduate and postdoctoral students, and senior researchers in mathematics, physics, and other relevant scientific areas.;

650 0 a| Bäcklund transformations.=| ^A91181;

650 0 a| Darboux transformations.=| ^A523152;

700 1 a| Yurov, Artyom.=| ^A1258311;

830 0 a| Surveys of modern mathematics ;v| v. 8.=| ^A1257461;

949 i| 30372016575968o| jjlm;

960 o| 1s| 58.00t| Joyner48u| JMATz| USD;

596 a| 1;

998 a| 3730236;

999 a| QA374 .L529 2014w| LCc| 1i| 30372016575968d| 4/26/2015l| JGESm| JOYNERr| Ys| Yt| JGESBKu| 4/23/2015x| BOOKz| JSTACKSo| .STAFF. jjlm;

Lie-bäcklund-darboux transformations / Y. Charles Li, Artyom Yurov.

Author/creator	Li, Charles, 1965-
Other author	Yurov, Artyom.
Format	Book
Publication	[Somerville, Mass. ; Beijing, China] : International Press and Higher Education Press, [2014]
Copyright Date	©2014
Description	ix, 160 pages : illustrations ; 26 cm.
Subjects	Bäcklund transformations. Darboux transformations.

Series	Surveys of modern mathematics ; v. 8 Surveys of modern mathematics ; v. 8. ^A1257461
Contents	1. Introduction -- 2. A brief account on Bäcklund transformations -- 3. Nonlinear Schrödinger equation -- 4. Sine-Gordon equation -- 5. Heisenberg ferromagnet equation -- 6. Vector nonlinear Schrödinger equations -- 7. Derivative nonlinear Schrödinger equations -- 8. Discrete nonlinear Schrödinger equation -- 9. Davey-Stewartson II equation -- 10. Acoustic spectral problem -- 11. SUSY and spectrum reconstructions -- 12. Darboux transformations for Dirac equation -- 13. Moutard transformations for the 2D and 3D Schrödinger equations --14. BLP equation -- 15. Goursat equation -- 16. Links among integrable systems.
Summary	This is an interdisciplinary monograph at the cutting edges of infinite dimensional dynamical systems, partial differential equations, and mathematical physics. It discusses Y. Charles Li's work of connecting Darboux transformations to homoclinic orbits and Melnikov integrals for integrable partial differential equations; and Artyom Yurov's work in applying Darboux transformations to numerous areas of physics. Of particular interest to the reader might be the brand-new methods, developed by Li in collaboration with others, of using Darboux transformations to construct homoclinic orbits, Melnikov integrals, and Melnikov vectors for integrable systems. It should be noted that integrable systems (also named soliton equations) are the infinite dimensional counterparts of finite dimensional integrable Hamiltonian systems. What the new methods reveal are the infinite dimensional phase space structures. This work is intended for advanced undergraduates, graduate and postdoctoral students, and senior researchers in mathematics, physics, and other relevant scientific areas.
Bibliography note	Includes bibliographical references (p. [155]-160) and index.
ISBN	1571462880
ISBN	9781571462886

Lie-bäcklund-darboux transformations / Y. Charles Li, Artyom Yurov.

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